In such a nursing bra it is generally convenient to arrange the openable flap in the upper flap of the cup and to provide it with a clasp allowing it to be releasably fastened to an associated connector which links an overlying part of the frame with a respective shoulder strap. Such clasps are already known in the art; reference may be made in this connection to U.S. Pat. Nos. 921,846 and 3,200,464, for example, as well as to my prior U.S. Pat. No. 4,000,544.